This is the company’s first quarter under new CEO Scott Thompson and comes after a tumultuous start to his tenure that has already featured a board shuffle, a proxy fight, a surprise patent lawsuit against Facebook and layoffs that cut Yahoo’s workforce by 14% — 2,000 workers.

Ad revenue is core to Yahoo’s business. The company’s revenue for the quarter (minus costs of traffic acquisition paid to partners) was $1.077 billion, and of that, $454 million — nearly half — was generated by display ads. The troubling stat in there is that while the overall market is growing, Yahoo’s revenue for the segment shrank by 4% (from $471 million) for the quarter year over year.

Then there’s perhaps the most damning stat of all: The company made more on its investments during the quarter ($172 million) than it did through operating income ($169 million).

In 2011, the ad-revenue growth leaders were Facebook, with 51.7% growth in revenue for the year, and Google (NASDAQ:GOOG), with 41.9% growth. Yahoo’s display-ad revenue, in comparison, shrank by 2.8%.

Projections for 2012 have both Google and Facebook looking at near-50% growth rates again, while Yahoo sits at around 4%. Even Microsoft (NASDAQ:MSFT) and AOL (NYSE:AOL) top Yahoo at expected revenue growth of 20% and 16%, respectively.

Lack of growth when competitors are going gangbusters means falling market share, and while Yahoo took in 9.5% of all online ad revenue in 2011, that percentage is projected to drop to 7.4% this year and 5.6% by 2014.

This is not a good trend for a company so dependent on ad revenue.

There is a danger that all of CEO Thompson’s streamlining efforts may bring only temporary relief if the problem in online advertising is not fixed. He seems to recognize this challenge and has publicly stated that he’s not happy with the overall results, a positive sign since he could have simply played up the fact that Yahoo (slightly) beat analysts’ expectations.

As reported in Forbes‘ coverage of Yahoo’s earnings conference call, Thompson commented: “Display revenue was down. Some positive signs on monetization, but our display business is nowhere near where it needs to be in any of our three regions.” When questioned about the mobile space, his response was frank: “We need to get good real fast in mobile. And we’re not there today.”

One slightly worrisome comment from the call came from Yahoo CFO Tim Morse, who suggested that Yahoo could pursue licensing of its patents to boost revenue. This isn’t necessarily a bad idea, except publicly stating this as a strategy sends a slightly desperate message, bringing Eastman Kodak (NYSE:EK) to mind.

Yahoo still has potential to turn things around.

As Thompson pointed out during the earnings call, Yahoo has 700 million users, significant cash flow and works with thousands of advertisers. And yes, it has patents it could monetize.

Focusing on Yahoo’s core properties by shutting down 50 units is a start. Thompson’s commitment to leveraging the personal data Yahoo collects to offer more compelling targeting capabilities for advertisers (including improved analytics for tracking performance) is a good measure.

This quarter’s earnings may have earned CEO Thompson and Yahoo a reprieve, but online ad revenue needs to show improvement before anyone gets too confident about Yahoo’s long-term prospects.

As of this writing, Brad Moon did not own a position in any of the stocks named here.